Super-Brownian motion as the unique strong solution to an SPDE

Jie Xiong

doi:10.1214/12-AOP789

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March 2013 Super-Brownian motion as the unique strong solution to an SPDE

Jie Xiong

Ann. Probab. 41(2): 1030-1054 (March 2013). DOI: 10.1214/12-AOP789

Abstract

A stochastic partial differential equation (SPDE) is derived for super-Brownian motion regarded as a distribution function valued process. The strong uniqueness for the solution to this SPDE is obtained by an extended Yamada–Watanabe argument. Similar results are also proved for the Fleming–Viot process.

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Jie Xiong. "Super-Brownian motion as the unique strong solution to an SPDE." Ann. Probab. 41 (2) 1030 - 1054, March 2013. https://doi.org/10.1214/12-AOP789

Information

Published: March 2013

First available in Project Euclid: 8 March 2013

zbMATH: 1266.60119

MathSciNet: MR3077534

Digital Object Identifier: 10.1214/12-AOP789

Subjects:

Primary: 60H15

Secondary: 60J68

Keywords: Backward doubly stochastic differential equation , Fleming–Viot process , Stochastic partial differential equation , Strong uniqueness , super Brownian motion